Wellbores are formed in subterranean formations for various purposes including, for example, the extraction of oil and gas and the extraction of geothermal heat. Such wellbores are typically formed using one or more drill bits, such as fixed-cutter bits (i.e., “drag” bits), rolling-cutter bits (i.e., “rock” bits), diamond-impregnated bits, natural diamond and hybrid bits, which may include, for example, both fixed cutters and rolling cutters. The drill bit is coupled either directly or indirectly to an end of a drill string or work string, which encompasses a series of elongated tubular segments connected end-to-end that extends into the wellbore from the surface. The wellbore is formed by rotating the drill bit so that its associated cutters or abrasive structures cut, crush, shear, and/or abrade away the formation materials, thereby facilitating the advancement of the drill bit into the subterranean formation.
As the drill bit progresses, differing formations formed of differing rock types that exhibit unique or differing hardness are often encountered. Relatively harder rock types can cause a drill bit to wear faster and can cause a slower drilling rate.
Moreover, the drill string is made of elastic materials, such as steel tubing, which are deformable under torsion. During drilling, the drill string can be elastically twisted by varying amounts, up to several full 360-degree revolutions, because of torsion created by the driving rotational force on the drill string and/or bit and the friction on the drill bit as it engages the underlying rock. The drill string also displays a complicated dynamic behavior comprising axial, lateral and torsional vibrations. In extreme cases, the torsional part becomes so large that the drill bit periodically comes to a complete standstill, during which the drill string is torqued-up until the drill bit suddenly rotates again at an angular velocity that is much higher than the angular velocity measured at the surface. This phenomenon is known as stick-slip, which causes excessive and unwanted vibrations for a drill string in the torsional direction.